Ask HN: Pure Math Problem
6 comments
"any number" means that you must be able to produce two triangles if asked for two, three if asked for three, four if asked for four, 7 trillion if asked for 7 trillion, etc. Effectively, you have to be able to generate infinitely many (technically: aleph-0) Pythagorean triangles.
Aside: I do not think that is a the nice problem, as there are way easier ways to generate aleph-0 such triangles (I think most mathematicians would agree the simplest is 3x,4x,5x for x in {1,2,...}) But that is not what this question is hinting at.
Aside: I do not think that is a the nice problem, as there are way easier ways to generate aleph-0 such triangles (I think most mathematicians would agree the simplest is 3x,4x,5x for x in {1,2,...}) But that is not what this question is hinting at.
It probably means that you need to use the given postulates and known theorems about right-angled triangles to come up with a way or formula for generating such triangles.
I'm guessing it means you have to come up with a generative process that produces k such shapes for any k.
think Pythagorean triples
If λ, m, and n are positive rational numbers, and m > n, then λ(m^2 − n^2), 2λmn, and λ(m^2 + n^2) are positive rational numbers. Hence show how to determine any number of right-angled triangles the lengths of all of whose sides are rational.
I'm not asking the solution, but I'm not sure what he means by "any number of right-angled triangles"